Case II: Let \(\min _{i\in \Sigma } \ell (x, i) < \max _{i\in \Sigma } \ell (x, i)\) . Following [1]} it follows that the predictor can be characterized equivalently as the convex continuously differentiable minimization problem
\(\hat{c}_{\mathrm {KL}}(x,\mathbb {P}, T)= \min _{\alpha \ge \gamma (x)} ~\lbrace f(\alpha ; x,\mathbb {P}, T):=\alpha - e^{-r} \exp (\textstyle \sum _{i\in \Sigma } \log \left(\alpha -\ell (x, i) \right) {\mathbb {P}(i)})\rbrace \) 
